1. **Problem statement:** Given the function $f(x) = 4x3^x$, find the value of $f(3)$. 2. **Formula and rules:** To find $f(3)$, substitute $x=3$ into the function. 3. **Substitution:** $$f(3) = 4 \times 3 \times 3^3$$ 4. **Evaluate powers:** $$3^3 = 27$$ So, $$f(3) = 4 \times 3 \times 27$$ 5. **Multiply:** $$4 \times 3 = 12$$ Then, $$12 \times 27 = 324$$ 6. **Final answer:** $$f(3) = 324$$ None of the given options (3, 4, 12, 64, 81) match 324, so the correct value is 324, which is not listed.